Solve the following fractional quadratic equation 14/(x^2-9)+1/(3-x)+(4-x)/(x+3)=7/(x+3), assuming x=/=+-3.

The first step is to find a common denominator. Since x^2-9 can be expanded to (x-3)(x+3) and 1/(3-x) can be written as -1/(x-3), we can see that all the terms contain either (x-3), (x+3), or both. Therefore the common denominator is the product of these two. Now we can rewrite the equation as follows: [14–(x+3)+(4-x)(x-3)]/(x-3)(x+3)=7(x-3)/(x-3)(x+3) Then we multiply both sides of the equation by the denominator, so we are left with the numerators only. 14-(x-3)+(4-x)(x-3)=7(x-3) The next step is to remove the brackets. 14-x+3+4x-x^2-12+3x=7x-21 Adding up the homogeneous expressions, we get: -x^2+6x-1=7x-21 -x^2-x+20=0 We can multiply this by (-1) if we want a nicer equation, or solve it straight away using the quadratic formula. The solution will be the same either case. As it is a quadratic equation, we always get 2 answers. These are x1=4 and x2=-5 here.